In order to check to what extent one can reduce unpleasant ”end effects”, the wall was first built with a constant laser power. In the upper panel of Figure 14, one can notice to wide ends of the wall. When the laser power was reduced each time when the laser head was near one of the endpoints (see Sec. 6.5) the resulting wall has more proper endpoints (see the lower panel of this figure). The wall has the length of about 60 mm. The speed of the laser head was about 10 mm/sec., while a stainless steel powder was supplied with the feed rate at 0.06 g/sec.
In fact, the wall at the lower panel of Figure 16 was obtained under more subtle, gradual change of the laser power, but this aspect is outside the scope of this paper.
Conclusions
Our first step was an attempt to provide some systematics for images and image sequences, from the viewpoint of their classification. At this stage, the class of images and image sequences having matrix (tensor) normal distribution was selected as sufficiently general, but still, a manageable class distribution. The MND class distributions have the covariance matrices that take into account only the inter-row and the inter-column covariances. Therefore, they are easier to estimate than in a general case. However, a specialized form of the covariance matrices leads to more specific classifiers than in the general case. Their structure was derived and their empirical forms were proposed as the classifiers for further investigations.
Finally, these classifiers were tested on the problem of detecting, from short image sequences, whether a laser head is near the endpoints of a cladding wall. In other words, the proposed classifier is used in the problem of change detection from image sequences. Its performance is quite satisfactory. Its behavior was also compared with a general purpose and widespread classifiers that do not take into account a special covariance structure or the class imbalance. As it was documented by the laboratory images, only 5-NN classifier can be comparable with the proposed approach since it is – to some extent – robust against a naïve learning.
Clearly, one can consider other methods for image feature representation and classification, e.g., in [47] the spectral and wavelet analysis as feature extraction techniques were employed, in [48] the feature extraction is based on a com-bination of a self-organized map used for image vector quantization and those generated by a neural network, a kernel sparse representation, which produces discriminative sparse codes to represent features in a high-dimensional feature space, is proposed in [49], while in [50] non-conventional approaches to feature extraction were proposed. A feature extraction is a common focal point of all these approaches. It is laborious, human-invented and dedicated to a particular application. In opposite, we stress that the proposed approach does not need a feature extraction step. Instead, “raw” images are supplied as inputs for a classifier, providing an acceptable level of proper classifications. This approach is less laborious, but its applicability is limited to cases when there is no need to consider very subtle differences between images.
The proposed approach may be useful, at least, at one more area of applications, namely, in using classifiers to detect states of industrial gas burners from image sequences (see [39]). It seems that further efforts are necessary in order to sketch a wider class of applications for which the proposed approach outperforms a general purpose classifiers when they are applied to image sequences.
Figure 14
Upper panel – the wall produced with constant laser power along the wall length. Lower panel – the wall produced with controlled laser power trajectory along the pass.
Acknowledgement
This research has been supported by the National Science Center under grant:
2012/07/B/ST7/01216.
Special thanks are addressed to Professor J. Reiner and to MSc. P. Jurewicz from the Faculty of Mechanical Engineering, Wroclaw University of Technology for common research on laser power control for additive manufacturing.
The author express his thanks to the anonymous reviewers for many suggestions, leading to the improvements of the presentation.
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